cp's OEIS Frontend

A296226 Decimal expansion of the limiting ratio of terms in A296225.

%I A296226 #11 Mar 15 2025 06:30:21
%S A296226 3,6,5,1,1,0,0,5,3,4,0,0,7,3,4,9,6,7,8,2,5,0,8,5,0,3,2,2,6,5,9,9,5,1,
%T A296226 9,5,4,5,0,2,4,1,4,6,0,5,4,1,7,8,1,3,0,0,7,4,7,9,7,0,8,2,6,2,7,8,8,7,
%U A296226 3,3,6,9,5,7,8,1,8,2,7,9,3,4,1,2,7,4
%N A296226 Decimal expansion of the limiting ratio of terms in A296225.
%C A296226 See A296000 for a guide to related sequences and limiting ratios.
%F A296226 Equals lim_{n->oo} A296225(n)/A296225(n-1).
%e A296226 3.651100534007...
%t A296226 mex[list_] := NestWhile[# + 1 &, 1, MemberQ[list, #] &];
%t A296226 a[0] = 1; a[1] = 3; b[0] = 2;
%t A296226 a[n_] := a[n] = n + Sum[a[k]*b[n - k - 1], {k, 0, n - 1}];
%t A296226 b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]];
%t A296226 Table[a[n], {n, 0, 200}]  (* A296225 *)
%t A296226 Table[b[n], {n, 0, 20}]
%t A296226 N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200];
%t A296226 RealDigits[Last[t], 10][[1]] (* A296226 *)
%Y A296226 Cf. A296000, A296225.
%K A296226 nonn,easy,cons
%O A296226 1,1
%A A296226 _Clark Kimberling_, Dec 10 2017